Optical connectors are known in several embodiments, for instance as described in British Pat. No. 1 478 135 and in U.S. Pat. No. 4,190,317. In the connector described in the British Patent the bushing is positioned at a considerable distance inside the mouth of the connector and is compressed axially in order to be expanded radially by means of a piston fixed within the connector by varnish, while the end of the optical fibre is, after the compression of the bushing resulting in the concentric fastening of the fibre, fixed by means of resin in the mouth of the connector. Besides being a relatively complicated construction accuracy is necessarily lost as a result of the spacing of the bushing from the mouth of the connector so that in all probability desired low optical damping can not be achieved. Errors in accuracy are also produced by the method described in said British patent since the free end will wobble during the turning of the surface, so that a different thickness of material is obtained in the bushing. The connector assembly described in said U.S. patent is also a relatively complicated construction. The bushing is tapered in order to hold the fibre after a forced insertion of the bushing into a narrow bore, which according to the preferred embodiment is made in a second bushing arranged in a recess in the mouth of the connector. Due to several details cumulative errors in accuracy are produced resulting in a deteriorated optical damping. During the force insertion of the tapered body there is also a risk of skew setting or "swelling" which also results in deteriorated accuracy.